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Fig. 4.11 a The thickness of congelation ice and snow-ice as a function of a fixed snow
accumulation; b The thickness of congelation ice and snow-ice as a function of density of new snow
and packing rate of snow. The air temperature corresponds to Oulu in the northern Finland
(Lepp ä ranta 1983)
When there is snow on the ice, its thickness and density need to be modelled. Snow
accumulation is given in terms of water equivalent, and the thickness and density of new
snow are obtained from
ˁ s0 h s' =
ˁ w h w . The density of new snow is assumed or parameterized,
100 kg m 3 . When the snow becomes older, its density increases due
to snowmetamorphosis, and old seasonal snowmay reach densities of 400 kg m 3 . Thermal
conductivity of snow is a sensitive function of density (see Sect. 3.2.3 ). The density change in
snow due to compaction is formulated after Yen (1981) as
ˁ s0 *
the magnitude is
@ q s
C 2 q s þ T f T a
12 : 5 C
@ t ¼ q s C 1 V s exp
ð
4
:
59
Þ
where C 1 = 7.0 m 1 h 1 and C 2 = 21.0 Mg 1 m 1 are empirical coef
cients, and V s is the
volume of overlaying snow in equivalent thickness of water. A depth-dependent snow
density pro
le due to snow compaction can be determined from this model.
ranta (1983) used a three-layer (congelation ice, snow-ice and snow) model to
examine the formation of snow-ice. A
Lepp
ä
fixed packing rate with the upper limit of
450 kg m 3 for the snow density was assumed. Figure 4.11 shows the model outcome for
the stratigraphy of the ice sheet and sensitivity of ice thickness to snow accumulation. The
representative heat
fl
flux from the water was estimated from ice and atmosphere
climatology.
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